Calculating An Actor’s Performance Expectation

James W. Balkwell
University of Georgia

     Status characteristics theory posits that perceived differences among the persons in a goal-oriented group engender differences in the performance expectations each person holds for the others, which in turn affect their respective rates of participation, influence, and certain other features of goal-related activity.  If John and Karen, for instance, are members of the group, then the early parts of their interaction will engender e_j and e_k, their respective performance expectations. Given this conception, it is important to measure e_j and e_k in a way that reflects the processes the theory posits.

     In this paper, I will address two problems: (1) how to calculate actors’ performance expectations, obtaining numerical values that may be entered into a research data file; and (2) how these values derive from the theory of status characteristics and social interaction. A great strength of the measure is its close logical relationship to some theoretical ideas, which themselves are consistent with, though not logically derivable from, understandings widely shared in social psychology, including those understandings most basic to the Cooley-Mead tradition.

     For the researcher, performance expectation values are simply an independent variable that permits her or him to predict relative rates of participation, deference, social influence, and related behaviors in an interacting group. For the theorist, however, these may seem suspect unless he or she understands how they reflect the processes believed to precede observable patterns of behavior. In the symbolic interactionist tradition, theorists have given much attention to the processes through which actors interpret their situations. Quite consistent with the symbolic interactionist conception, status characteristics theory posits a sequential processing of social information that results in a set of shared attributions to a group’s members. To a considerable extent, the processes involved are shaped by the limits of human information-processing and by the external constraints of task situations.

The Essential Ideas

     The theory of status characteristics and social interaction (Berger, Fisek, Norman, and Zelditch 1977) posits that the actors in a task-oriented situation (say, in a committee meeting) form performance expectations for themselves and each other. These expectations are part of their completed definition of the situation, helping to guide them as they conduct their activity. In content, these are implicit evaluations of the respective actors’ capabilities, relative to what is typical among members of the group, for getting the job done or for contributing to this effectively. If others attribute to an actor an expectation of zero, this would mean that others expect the actor in question to be neither more nor less effective than most others in contributing to the group’s success. An actor for whom others anticipate above-average contributions would have a positive expectation, and one for whom others anticipate below-average contributions would have a negative expectation. This conception of expectations as relative means that the average expectation within the group is zero, though some members may have positive expectations and others negative expectations, reflecting their differences on perceptible characteristics.

     This paper focuses upon Berger et al.’s (1977) measure of performance expectations, showing how to obtain numerical values on this measure for the actors in a situation. In principle, the theory applies to n-person groups, but the measure is best developed for task-oriented dyads. (Efforts to generalize it to larger groups are ongoing, but will not be dealt with here.)

Paths of Relevance

     Consider a relatively simple situation entailing two actors, p and o, working together on a task, T. By convention, p is the actor upon which the analysis focuses, although either person in a real dyad could be taken as p. Let C* denote the talent or ability instrumental to success at T. And suppose that p possesses a relatively high level of C*, while o possesses a relatively low level, these being the attributions of the actors in the situation. (This notation is fairly standard in the literature.) By hypothesis, we can diagram the focal actor’s initial definition of the situation as follows.

Figure 1. Illustrative relevance diagram

     This diagram represents some essential elements of the situation, an initial stage in an actor’s definition of the situation, which he or she will translate into a simpler, more refined, and more useful definition through cognitive information processing. Among the results of this processing will be e_p and e_o, performance expectations for the two actors in question. Because these performance expectations are relative to each other, e_p + e_o ≡ 0. Much of the status characteristics literature emphasizes an actor’s expectation advantage over a second actor, defined as e_p – e_o, a feature of the actors’ shared definition of their situation that partly shapes their pairwise interaction. In dyads, it is necessarily the case that e_p – e_o ≡ 2e_p and that all the interaction is pairwise.

     In this diagram, p is connected to the possible task outcomes by two positive paths of lengths 2 and 3, while o is connected by two negative paths, also of lengths 2 and 3. Verbally: (1) “p has a high level of the task ability, which is associated with success at the task,” (2) “p has a high level of the task ability, which is the reverse of a low level, which is associated with failure at the task,” (3) “o has a low level of the task ability, which is associated with failure at the task,” and (4) “o has a low level of the task ability, which is the reverse of a high level, which is associated with success at the task.” The length of a path corresponds to its number of lines.

     The lines have signs, + or – , associated with them. When a line corresponds to the phrase, “is the reverse of” [for instance, the line between C*(+) and C*(–)], its sign is negative. In all other cases, its sign is positive. Dimensionality relations (those with minus signs) exist only between oppositely evaluated states of a status characteristic that is possessed by some group member.

     The sign of an entire path is obtained by multiplying the signs of its segments and the sign of the task outcome at the end of it, using a rule analogous to that of ordinary algebra for multiplying signed numbers. For the respective paths of my example, (+)(+)(+) = (+), (+)(–)(+)(–) = (+), (+)(+)(–) = (–), and (+)(–)(+)(+) = (–). Thus, p’s two paths are positive, and o’s two paths are negative. While this rule is mechanical, it is important to recognize that it yields results that make good sense: a positive path is a chain of associations with positive implications for an actor’s likely task performance, a negative path being one with negative implications for that person’s likely task performance. The mechanical nature of the rule should not obscure the essential point that its results make sense.

     It is important to distinguish between positive and negative paths because the subsets of each person’s paths defined by this distinction (four subsets in all) must be dealt with separately in computing p’s expectation advantage. This need for separate consideration derives from the principle of organized subsets, a substantive principle of the theory which asserts that information that would raise an actor’s performance expectations is combined together, information that would lower those expectations is combined together, and these results are weighed in the final stage. We can imagine this being like a balance with two pans dangling from a bar with a fulcrum at the center, one pan for the factors contributing to likely performance, the other pan for the factors detracting from likely performance.

Combined Strength of a Subset of Paths

     The theory thus requires us to find separately the combined strength of an actor’s positive paths and the combined strength of her or his negative paths. In making the computations for obtaining e_p – e_o, it is helpful to organize the calculations for these subsets in accordance with a table such as the following:

     In the Berger et al. theory, f(i) is the strength of a path of length i, which is conceptualized as a real number between zero and one.

     Path-lengths less than 2 or greater than 6 are not represented in this table because such paths do not enter into our calculations. An actor’s association with a task outcome must be mediated by at least one other cognitive element, which means that a path will always be at least two lines long. Paths of length 6 are extremely rare in the published literature. Although paths of seven lines or more are logically possible, a path of length 7 may be presumed to have a strength that is practically zero, which means that such paths may be disregarded. In general, the longer a path, the less its strength. In more intuitive terms, the longer a chain of associations, the more tenuous the inferences it permits about an actor’s capacity to contribute to the success of the group’s work.

     The combined strength of any applicable subset of paths is calculated from the following equation:

     An actor’s expectation state value is the combined strength of her or his positive paths (calculated from the equation above), minus the combined strength of her or his negative paths (calculated separately from the equation above). For Actor x, if we denote the results of these respective calculations e_x+ and e_x–, the actor’s expectation state value e_x is:

Expectation Advantage:  e_p – e_o

     Much of research literature reports studies of dyads or pairs of actors who are working together on a task, the independent variable being the expectation advantage of the focal actor over her or his partner.  We find by subtracting the second actor’s expectation state value from that of the first (i.e., focal) actor. To illustrate all this, consider the two actors and the situation diagrammed in Figure 1:

e_p+ = 1 – {[1–f(2)]¹ [1–f(3)]¹ [1–f(4)]⁰ [1–f(5)]⁰ [1–f(6)]⁰}

= 1 – {[1–f(2)] × [1–f(3)] × 1 × 1 × 1}

= f(2) + f(3) – f(2) × f(3)

e_p– = 1 – {[1–f(2)]⁰[1–f(3)]⁰ ... [1–f(6)]⁰}

= 1 – {1 × 1 × 1 × 1 × 1}

= 0

e_o+ = 1 – {[1–f(2)]⁰[1–f(3)]⁰ ... [1–f(6)]⁰}

= 0

e_o– = 1 – {[1–f(2)]¹[1–f(3)]¹[1–f(4)] ⁰ ... [1–f(6)]⁰}

= f(2) + f(3) – f(2) × f(3)

     After these four results have been obtained, we can compute each actor’s expectation state value, and each actor’s expectation advantage vis-a-vis the other for the experimental condition in question. If p is the focal actor, her or his expectation advantage is:

     This formula shows us that p’s expectation advantage is enhanced by o’s negatively evaluated status characteristics, as well as by his own positively evaluated status characteristics.  It is diminished by o’s positively evaluated characteristics, as well as by his own negatively evaluated characteristics. Formula [3] also implies that p’s “advantage” may be negative—that is, it may be a disadvantage.

Values of the f(j) Terms

     We have been assuming that the f(i) quantities have definite numerical values. The question now is: How can we obtain those values? The 1977 version of the theory treated these quantities as parameters to be estimated from the research data. In the 1977 book, only two of these parameters were considered independent, due to a theoretical relationship involving them. This theoretical relationship can be stated as follows: There exists some fixed number k such that, for all permissible values of j,

     More recently, there have been at least two efforts to find a priori values, as opposed to empirically estimated values (see Balkwell 1991; Fisek, Norman, and Nelson-Kilger 1992). For the analyses I have done in the past, I have employed a priori values I believe have some merit. Presently, I wish to present these values and the rationale for them.

     Given the constraint stated in formula [4], we can derive that, for all permissible values of i, and for every positive integer n, the following holds true:

     As I suggested above, researchers long have assumed that the hypothetical path-strength f(1) is close to one, and that f(7) is close to zero. Intuitively, an association would not exist unless the actor in question were nearly certain of it (e.g., that someone who appears female really is female, or that a high level of the instrumental ability really is associated with success at the task). At the other end, a path of length seven would be so indirect as to have little significance. I am not certain if the research literature contains an example of a path of length seven. Rarely do we find paths longer than five. Suppose that f(1) = 0.995 and f(7) = 0.005. Now take i = 1 and n = 6 in formula [5] above; and substitute the postulated values of f(1) and f(7). Solving for k⁶, we find that k⁶ = 1057; therefore, since k must be positive, k = 3.192.

     From this reasoning, we have values of f(1), f(7), and k. From the last two of these, using formula [3], we can calculate f(6). From f(6) and k, we can then calculate f(5). From f(5) and k, we can then calculate f(4). And so on. Carrying out these calculations to many significant digits of accuracy, I obtained the following set of path-strength values:

     That these values, based partly on a priori considerations, are not too far from the empirical estimates reported by Berger et al. (1977:144) gives them further credibility. By the same token, it is encouraging that Berger et al.’s empirical estimates were consistent with plausible assumptions about path-lengths outside the range normally employed to calculate e_p – e_o.

     Returning to the simple illustration presented earlier in this essay, we find:

e_p+ = f(2) + f(3) – f(2) × f(3)

= 0.80987 + 0.40556 – (.80987)(.40556)

= 0.88698

e_p– = 0.000000

e_o+ = 0.000000

e_o– = 0.88698

Now using formula [3], the formula for an actor’s expectation advantage, we get:

e_p – e_o = (0.88698 – 0.00000) – (0.00000 – 0.88698)

= 1.77396

     This, then, is the value of p’s expectation advantage for a situation like that described. It is easily verified that e_p – e_o = 2 e_p (as will always be true in dyads).

     For many situations, the graph hypothesized to represent the focal actor’s initial definition of the situation should include multiple status characteristics, specific and/or diffuse. The members of a group might be differentiated by age, gender, race, and various specific abilities, as well as by the instrumental ability. In some cases, this graph should include actors besides p and o, and in some it should include aspects of reward systems imported from the larger cultural or structural context. The principles illustrated in this essay are by no means limited to simple cases like the one of my example. They can be applied to much more elaborate cases as well.

Program for Calculating e_x

     Equations [1] and [2] are easily programmed. Once an actor’s set of inferential paths has been represented with an appropriate diagram, and the numbers of positive and negative paths of different lengths have been counted, the rest is straightforward, although it can be tedious if we must do the calculations by hand. The program that follows helps relieve the burden of what otherwise would be tiring and error-prone hand calculations.

     We assume here that e_x (x being the actor of interest) is the quantity whose numerical value we want. Typically, x would be p, the focal actor in a particular experimental condition.  The input is eight numbers, specifically, that actor’s numbers of paths of lengths two, three, four, and five, counted separately for positive and negative paths. To get the focal actor’s expectation advantage over the other actor, if that is the quantity we desire, it normally suffices to double e_p, for the reasons explained earlier, namely, that e_p + e_o = 0 implies that e_p – e_o = 2 e_p.

     For the focal actor, enter the information requested, then click the button below. Be sure to enter zero for each item for which the focal actor has no paths of the given sign and length.

Note.—To get an actor’s expectation advantage, it normally suffices to double this value (see the explanation above).

Status Processes in More Complicated Groups

     The goal-oriented groups we most want to understand are corporate committees, government panels, juries, and other groups that make decisions affecting many people’s lives.  Status characteristics theory posits that structural and cultural features of the organizations and communities within which these groups operate are imported into the local settings of these groups, where they partially determine sets of performance expectations and, through those, the groups’ decisions and other outcomes.

     Balkwell (ASR, June 1991) sought to predict rates of participation in Bales-type discussion groups ranging in size from two to eight persons.  The prediction equation used in this investigation was:

In this expression, x_i is a dummy variable representing the i-th person’s acceptance as the group’s legitimate leader, and m and q are unknown constants that must be estimated from the research data.  Each of the k persons in the group has a performance expectation, denoted e_i for the i-th person.   In groups of two to eight persons, this function predicted the observed rates of participation remarkably well.

     Because Bales-type discussion groups are initially undifferentiated and homogeneous with respect to recognized status characteristics, Balkwell was able to make some very simple assumptions in order to calculate the e_i quantity for each person in the group.  Looking to the future, however, and studies of more complicated groups, an important challenge will be to find appropriate “relevance diagrams” (extensions of that in Figure 1).  Once that is done, the principles for calculating performance expectations explicated in this paper should apply straightforwardly.

05/16/2000 6:41 p.m.   Contact the author at balkwell@uga.edu.